pub fn new_birthday_probability(n: u32) -> f64 {
    if n >= 365 {
        return 1.0;
    }
    let mut prob = 1.0;
    for i in 1..n {
        prob *= (365 - i) as f64 / 365.0;
    }
    // only four number after the decimal point
    ((1.0 - prob) * 10000.0).round() / 10000.0
}
